Is there any reason an exchange operator couldn't create an account and sell a bunch of "fake" bitcoins? By "fake" I mean just setting bitcoin_balance in the database to 1,000,000 without actually having any bitcoins. As long as they stayed on the exchange everything would be fine. That is until they didn't have enough "real" bitcoins to cover transfers. I don't believe that's happening, but I'm just trying to convince myself for sure.
You're closing in on the idea that was probably the most significant to the history of banking after the invention of money itself.
Fractional reserve banking.
To the extent that an exchange like MTGOX is being used as a place to just park funds, they are in a position to do that. They have both a cash reserve and a BTC 'reserve.'
For example, they could invest some of the cash deposits and earn interest. Some of their depositors money probably already sits in something like a savings account generating interest for MTGOX. A somewhat more aggressive approach would be buying things like bank CDs with a slightly higher interest rate, which could be sold in a short amount of time if they needed the cash to cover depositors demanding their funds.
They might also explore the idea of making 'Bitcoin loans' but that is probably a bit too ridiculous for them to consider at this moment, given all that would have to be involved in the process for it to work, and that they clearly have their hands full for the time being.